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Cogito

Integrated Math 2 · Chapter 6 · Lesson 3

Practice Worksheet

Equations of Circles

A circle written in coordinates.

12 problems · about 21 minutes · G-GPE.A.1

NameDate

Figure — use these to answer the problems

Change the radius. In an equation this is the number whose square sits on the right side.
d = 10
  • Diameter10 cm
  • Circumference31.42 cm
  • Circumference ÷ diameter3.14
Radius5
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. (x − 3)² + (y − 2)² = 16. What is the radius?

    Answer

  2. Where does the circle equation come from?

    • The distance formula, applied to a fixed distance from a centre.
    • It is an unrelated definition.

  3. x² + y² = 36. What is the radius?

    Answer

  4. (x − 4)² + y² = 25. Radius?

    Answer

  5. Same circle. Centre x-coordinate?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. (x + 5)² + (y − 1)² = 9. Centre x-coordinate?

    Answer

  2. To complete the square on x² − 6x, what is added?

    Answer

  3. x² + y² = 0. How many points does the graph contain?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Put the steps for finding a centre from general form in order.

    Write 1 to 4 in the boxes to put these in order.

    • Group the x terms and the y terms.
    • Move the constant to the right.
    • Complete the square on each group, adding to both sides.
    • Read the centre and take the root of the right side.

  2. (x − 1)² + (y + 3)² = 64. Radius?

    Answer

  3. The Radius

    (x − 2)² + (y − 5)² = 49. What is the radius?

    Answer

  4. The Centre

    Same circle. What is the x-coordinate of the centre?

    Answer